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The Zero Divisor Graph of the Ring Zqp.
Science Journal of University of Zakho, 2015 In this paper we construct a star zero divisor graph from the zero divisor graph of the ring Zqp. The star zero divisor graph is obtained by removing some vertices from the zero divisor graph Γ(Zqp), in different ways , but the best way to get star zero ...
Nazar H. Shuker, Payman A. Rashed
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The wiener index of the zero-divisor graph for a new class of residue class rings [PDF]
Frontiers in Chemistry, 2022 The zero-divisor graph of a commutative ring R, denoted by Γ(R), is a graph whose two distinct vertices x and y are joined by an edge if and only if xy = 0 or yx = 0.
Yinhu Wei, Ricai Luo
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Non Deterministic Zero Divisor Graph [PDF]
Ratio Mathematica, 2023 A non-deterministic zero divisor graph refers to an element in a ring or algebraic structure that can multiply with another element to give zero, but the specific outcome of the multiplication is not uniquely determined.
Shakila Banu, Naveena Selvaraj
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Zero Divisor Graph of Quotient Ring [PDF]
Cauchy: Jurnal Matematika Murni dan AplikasiRecently, a lot of research has been carried out regarding graphs built from algebraic structures, including ring structures. One important example of a graph constructed from a ring is the zero divisor graph.
Ayunda Faizatul Musyarrofah +2 more
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Harary index of the zero divisor graph of upper triangular matrices [PDF]
Scientific ReportsThe Harary Index is an important topological parameter for examining the structure of a graph. This work presents a quantitative analysis of the structural features of zero-divisor graph using the Harary Index.
Omaima Alshanqiti +2 more
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A graph-theoretic approach to ring analysis: Dominant metric dimensions in zero-divisor graphs [PDF]
HeliyonThis article investigates the concept of dominant metric dimensions in zero divisor graphs (ZD-graphs) associated with rings. Consider a finite commutative ring with unity, denoted as R, where nonzero elements x and y are identified as zero divisors if ...
Nasir Ali +4 more
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On Normalized Laplacian Spectra of the Weakly Zero-Divisor Graph of the Ring ℤn
Mathematics, 2023 For a finite commutative ring R with identity 1≠0, the weakly zero-divisor graph of R denoted as WΓ(R) is a simple undirected graph having vertex set as a set of non-zero zero-divisors of R and two distinct vertices a and b are adjacent if and only if ...
Nazim, Nadeem Ur Rehman, Ahmad Alghamdi
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A note on the zero divisor graph of a lattice [PDF]
Transactions on Combinatorics, 2014 Let $L$ be a lattice with the least element $0$. An element $xin L$ is a zero divisor if $xwedge y=0$ for some $yin L^*=Lsetminus left{0right}$. The set of all zero divisors is denoted by $Z(L)$.
T. Tamizh Chelvam , S. Nithya
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Note on Ideal Based Zero-Divisor Graph of a Commutative Ring
Discussiones Mathematicae - General Algebra and Applications, 2017 In this paper, we consider the ideal based zero divisor graph ΓI(R) of a commutative ring R. We discuss some graph theoretical properties of ΓI(R) in relation with zero divisor graph.
Mallika A., Kala R., Selvakumar K.
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A Study on the Structure of Ideal-Based Non-Zero Divisor Graphs Associated with Zn [version 1; peer review: 2 approved] [PDF]
F1000ResearchBackground The study of algebraic structures through graph-theoretic representations provides a powerful visual and combinatorial framework for analyzing ring-theoretic properties. The ideal-based non-zero divisor graph ∅ I ( Z n ) , constructed from the
Ali Abd Aubad, Sameer Kadem
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